The value of x that satisfies the relation `x=1 -x+x^2-x^3+x^4-x^5+….oo is `

Options

A. `2 cos 36^@`
B. `2 cos 144^@`
C. `2 sin 18^@`
D. `2 cos 18^@`

Answer

C

Explanation

`x=1-x+x^(2)-x^(3)+x^(4)-x^(5)+..oo`
`thereforex=1/(1+x)`
`rArrx^(2)+x-1=0`
`rArrx=(-1pmsqrt5)/2`
But for infinite G.P., x=`(-1-sqrt5)/(2)` is rejected.
`thereforex=(-1+sqrt5)/2=2sin18^(@)`